Dislocations in covalent materials: the puzzling complexity of - - PowerPoint PPT Presentation

Laurent Pizzagalli GDR PULSE 2017

Dislocations in covalent materials: the puzzling complexity of cores.

Laurent Pizzagalli

Institut P', CNRS, Poitiers University, France

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Part I Dislocations in III-nitrides Stoichiometry + structure = diversity

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

III-nitride compounds (GaN, AlN, InN) and dislocations

• A. Mogilatenko et al., J. Cryst. Growth (2014)

The presence of dislocations can degrade (or even suppress) opto- electronics properties → Calculations to evaluate/predict/understand the influence of dislocations

Threading dislocations

Applications of III-nitride compounds concern for instance LED (AlN) and PV (InN)

• N. Lobo Ploch, PhD thesis (2015)

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Dislocations in GaN

• M. Matsubara et al., Appl. Phys. Lett. (2013)

Dislocation core structures for AlN and InN in different growth conditions? Influence of the most stable cores on electronic properties?

Ga-rich conditions

• J. Northrup et al., Phys. Rev. B (2002)

N-rich conditions Different dislocation core positions and stoichiometries lead to multiple configurations

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Dislocation modeling: Full PBC system

2 dislocations with opposite Burgers vectors Non-orthogonal periodic conditions

Initial conf. from elasticity theory

DFT calculations

Quantum Espresso code Plane-waves basis, cutoff 40 Ry PAW GGA-PBE 3 special k-points (disl. line)

For electronic structure:

HSE06 hybrid calculations 4 special k-points (disl. line)

Dependence on supercell size: 128/288 atoms

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Investigated dislocation cores: A-type Dislocation centered on one hexagon Initial configurations from a full Al core to a full N core

×

Al N

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Investigated dislocation cores: B-type

×

Al N Dislocation centered between two hexagons Initial configurations from a full Al core to a full N core

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Energy considerations

μmax (calc.) μmax (exp.)

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Energy considerations Non-stoichiometric configurations are favored for both Al-rich and N-rich conditions An open depleted core (minimal core distortions) is found in mid-range

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Electronic structure: Al-rich conditions Presence of metallic states associated to Al core atoms (Al-Al distance like in bulk Al), deep into the gap. Possible leakage currents along the dislocation line (like in GaN)

HSE06 calc.

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Electronic structure: intermediate conditions Presence of shallow states on Al-atoms and of deep empty states on N- atoms: possible non negligible influence on electronic properties

HSE06 calc.

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Electronic structure: N-rich conditions Deep states associated to triple bonds between core N atoms

HSE06 calc.

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Energy considerations: InN Non-stoichiometric configurations are favored for In-rich and mixed conditions A stoichiometric configuration is obtained in N-rich conditions

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Comparison between III-nitrides III-rich conditions: metallic-like III-filled dislocation cores N-rich conditions (GaN/InN): open (AlN, GaN) or filled (InN) bond-centred core, according to strength of bonds N-rich conditions (AlN): N-filled core only for AlN (high formation enthalpy)

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Part I conclusions Structure and stability of dislocation cores in III-nitrides

In III-rich conditions, a core filled with atoms III (Al, In, Ga) is found as the energetically most stable one. Metallic-like states are associated to this core, which could be a source of leakage currents In intermediate conditions, a bond-centered core, depleted (for AlN) or filled with In, is found. In N-rich conditions and AlN, two original N-filled cores are predicted to be more stable. These cores are characterized by the presence of N-N triple or double bonds. Associated electronic levels are located deep into the electronic gap.

• L. Pizzagalli et al., Phys. Rev. Materials 2, 064607 (2018)

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Part II Dislocations in silicon The plot thickens

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Si 1050°C

Dissociated dislocations Partials with 30° and 90° orientations High activation energies for mobility (Q ≈ 2.2 eV) Peierls mechanism : thermally activated formation/migration of kinks

30° 90° sp 90° dp

Dislocation core structure is known from calculations

Duesbery, Jones, Heggie, Bulatov, Yip, Vanderbilt, Jacobsen, Sutton, Payne, Sankey, Öberg, Kaxiras, and many others

High-temperature plasticity of (ductile) silicon

→ T wo quasi-degenerate core structures for 90° partial dislocations → Anti-phase defects (solitons) likely along dislocation line → High number of possible confjgurations / mechanisms for kinks → Few theory works on the interaction with impurities: Jones, Heggie, Ewels, Justo

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Non-dissociated dislocations Screw (wavy), 60°, 30°, and 41° orientations

Rabier et al MSE (2004) Izumi et al PML (2010)

Plastic deformation at low temperature / high stress

Rabier et al PSS (2007)

High stresses, about 1-1.5 GPa

• J. Rabier et al., in Dislocations in solids, vol 16, ch. 93, p47 (2010)

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

2 possible screw dislocation cores C2 is more stable but less mobile Nucleation/mobility → A is dominant

C2 A G S3 S1

X X

2 stable sessile 60° cores 1 transient mobile core

State of the art, until recently…

• L. Pizzagalli et al., Phys. Rev. Lett. 103, 065505 (2009)

Low temperature high stress Little importance for “bulk” applications Great importance for nanostructures (nanowires, fjlms)

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Plastic deformation of silicon nanostructures

• F. Hoffman et al., Adv. Func. Mat. (2009)

Kizuka et al., PRB (2005) Wagner et al., Acta Mat. (2015)

Nano-objects have been elastically deformed up to very large strains (>10%) A brittle-ductile transition is observed for small sizes Influence of large strains on dislocation cores Could a dislocation core leads to crack initiation? local disorder?

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Dislocation modeling: hybrid cluster-PBC system

Initially locked in positions given by anisotropic elasticity theory Allow for applying strain Ease electronic structure calculations

Only one dislocation in the supercell The dislocation-surface interaction must be negligible

DFT calculations

Quantum Espresso code Plane-waves basis, cutoff 20 Ry PAW LDA 2 special k-points

336 atoms DFTB calculations

DFTB+ code pbc-0.3 Slater-Koster parameters 5 special k-points

Potential calculations

SWm (L. Pizzagalli et al, JPCM 2013) MEAM (J. Godet et al, EML 2016) Tersoff (J. Tersoff, PRB 1989)

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Bi-axial strain deformation approach All 5 core geometries have to be tried for each strain state Strain the initial configuration

↓

conjugate gradient relaxation No Poisson relaxation along z (negligible influence)

εy εx

We do not know the most stable structure

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

60° dislocation core

S1 S2 S3 The 'traditional' core Stable with potentials Unstable with DFT Weakly stable with DFT Stable with DFT Sessile!!! S5 S4 Closed core Open core

All 5 cores must be computed for each stress state

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Bi-axial strain deformation map for the 60° dislocation The most stable dislocation core depends on the strain state

S1 S2 S3 S4 S5 Amorphization

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Initiation of crack S3 is the most stable for moderate tension

The transformation dislocation core → crack is possible for tensile strains occuring in experiments Bi-axial tension

(7.5%,7.5%)

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

S4 could be the most stable conf. Local disorder

The most stable dislocation core depends on the strain state The transformation core → disorder occurs for moderate compression Bi-axial compression

(-5%,-5%)

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

S1 can be stabilized

The most stable dislocation core depends on the strain state X-compression / Y-tension or X-tension / Y-compression

(-5%,5%) S2 can be stabilized too (5%,-5%)

• L. Pizzagalli et al., Philos. Mag. 98, 1151 (2018)

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Compression of small Si nanocubes/nanospheres Fingerprint of stacking faults Suggests partial dislocations in Si at RT ?

Wagner et al., Acta Mat. (2015)

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Compression of thin Si nanopillars

Experiments (coll. M. Texier et al.) Simulations (MD)

Evidence of stacking faults in both exp and MD Partial dislocations at low temperature in Si !!!

• M. Texier et al., submitted to Acta Materialia. (2018)

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Compression of thin Si nanopillars

“super-partial’

Superpartials b=1/3<112> Combination of two 1/6<112>,

• ne in shuffle, the other in glide

Already “observed” in 2004, but too surprising to be deemed correct!

• J. Godet et al. Comput. Mat. Sci. (2004)

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Compression of thin Si nanopillars Sessile S3 dislocation, dissociate into two partials, one in glide (Shockley), and the other in shuffle (“new” dislocation core)

• M. Texier et al., submitted to Acta Materialia. (2018)

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Compression of thin Si nanopillars A super partial can also dissociate in a fast moving shuffle perfect dislocation (S1), leaving a slow moving glide partial dislocations

• M. Texier et al., submitted to Acta Materialia. (2018)

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Plastic deformation of nanostructure → nucleation of new dislocations Nucleation of V-shaped (or split) dislocations > half-loop for Ge/Si thin films Only favored with DFT corrections

• E. Maras et al., Scientifjc Reports (2017)

Also observed in Si nanoparticles Efficient relaxation of bi-axial strain

• D. Kilymis et al., submitted to Acta Mat (2018)

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Part II conclusions

The core structure of a dislocation strongly depends on the strain state, resulting in different geometries, for strain levels of about 5%. In compression, a dislocation core could also lead to a locally disordered state. At large tensile strains, the dislocation core could transform into an opening, initiating a crack. New dislocation cores are identified, in nanostructures, due to high stress conditions Initiation of plastic deformation in nanostructures → New mechanisms (V-shaped, {110} dislocations), influenced by size and shape of the systems.

Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

The end

Julien Godet, Sandrine Brochard, Christophe Tromas, Ludovic Thilly, Jacques Rabier (P’ - Physics) Dimitrios Kilymis, Celine Gerard (P’ - Mechanics) Jonathan Amodeo (MATEIS, Lyon) Michael Texier, Amina Merabet, Olivier Thomas (IM2NP, Marseille) Joseph Kioseoglou (Aristotle University, Thessaloniki) Jun Chen (CIMAP, Caen) Imad Belabbas (Bejaia University, Algeria)

Thank you for your attention